# Data Analysis

I am attempting to process V & Ic data accumulated over 4 years (~ 3300 TS observations each filter) on a Delta-Scuti target.

I have both Peranso and Period04 pgms but am attempting to process all data with Period04 for this specific target as a single filter, single year study has already been published by another author using Period04 (as well as many other authors when analyzing Delta-Scutts).

I have hit a brick wall with the SNR calculation and hope that someone can steer me in the right direction, especially given the importance of the Breger constraint (statistical significance).

[Doug Welch has been kind enough to offer an alternative measurement approach to statistical significance but I would like to resolve my issues with Period04 in any event]

The below was copied from a paper that I have now replaced but is an example of of SNR calculation using period04:

“In order to search for statistically significant frequency in the time series data, we have used the criterion of Breger etal. (1993) that an amplitude signal to noise ratio (SNR) should be greater than 4.0to judge the reality of a peak in the amplitude spectrum. It consists of calculation of the SNR of the frequency in the periodogram. This is done by finding the highest amplitude of the peak for the frequency obtained and the noise as the average amplitude in the residual periodogram in a frequency range that encloses the detected peak after the detected frequency is pre-whitened. In Fig. 2, we show the amplitude spectrum of the HD 40372 obtained from Period04. The amplitude spectrum peaks at 15.36492 ± 0.02106 c/d with amplitude 0.01232 ± 0.00010 mag (upper panel). Also shown is the corresponding noise level of the peak. The noise level is at 0.00098 mag yielding a SNR of 12.620. The noise level is calculated in the frequency range from [frequency-boxsize/2.0 ,frequency+boxsize/2.0]. We have chosen boxsize = 20. We have also detected another frequency at 11.52369 c/d (lower panel of Fig. 2). SNR of this peak is 4.0.”

Given the data in the above example I am darned if I can arrive at their answer for SNR.

Can anyone help me with what formula they are using?

I note that Period04 has an option to "Calculate Noise At Frequency," under the Special menu, that produces a snr measurement as well as the noise calculation.

Is this the same SNR calculation as in the above example?

Also, in using this tool (Calculate Noise At Frequency) should the primary freq calculation also be based upon selecting the residuals at original?

Tim Crawford, CTX

Hi Tim,

Yes, that is the same calculation. You should indeed use the "Residuals at original" option.

I don't think the S/N>4 limit should be taken as a hard limit though. Some frequencies may have a higher S/N while they are still not genuine pulsation frequencies of the object. Other criteria may give indications as well: the frequency should be present in different filters and in different subsets (e.g. from year to year).

Patrick